A census of critical sets in the Latin squares of order at most six

A critical set in a Latin square of order n is a set of entries from the square which can be embedded in precisely one Latin square of order n, Such that if any element of the critical set. is deleted, the remaining set can be embedded, in more than one Latin square of order n.. In this paper we find all the critical sets of different sizes in the Latin squares of order at most six. We count the number of main and isotopy classes of these critical sets and classify critical sets from the main classes into various strengths. Some observations are made about the relationship between the numbers of classes, particularly in the 6 x 6 case. Finally some examples are given of each type of critical set.

Grand canonical Monte Carlo simulation study of methane adsorption at an open graphite surface and in slitlike carbon pores at 273 K

Grand canonical Monte Carlo (GCMC) simulation was used for the systematic investigation of the supercritical methane adsorption at 273 K on an open graphite surface and in slitlike micropores of different sizes. For both considered adsorption systems the calculated excess adsorption isotherms exhibit a maximum. The effect of the pore size on the maximum surface excess and isosteric enthalpy of adsorption for methane storage at 273 K is discussed. The microscopic detailed picture of methane densification near the homogeneous graphite wall and in slitlike pores at 273 K is presented with selected local density profiles and snapshots. Finally, the reliable pore size distributions, obtained in the range of the microporosity, for two pitch-based microporous activated carbon fibers are calculated from the local excess adsorption isotherms obtained via the GCMC simulation. The current systematic study of supercritical methane adsorption both on an open graphite surface and in slitlike micropores performed by the GCMC summarizes recent investigations performed at slightly different temperatures and usually a lower pressure range by advanced methods based on the statistical thermodynamics.

Van der Waals interactions between two parallel infinitely long single-walled nanotubes

The potential energies of van der Waals (VDW) interactions between two parallel, infinitely long and perfect SWNTs with identical, and different sizes were studied based on the continuum Lennard-Jones model. The conclusion of Girifalco's work on (n, n) SWNTs that the potentials of SWNT-SWNT fell on a single curve, is also applicable to SWNTs with different sizes. We further obtained the corresponding constants of the well depth phi(0) and equilibrium VDW gap g(0) for SWNTs with a radius from 2 to 25 Angstrom. (C) 2005 Elsevier B.V. All rights reserved.

Automatic building detection using the Dempster-Shafer algorithm

An approach and strategy for automatic detection of buildings from aerial images using combined image analysis and interpretation techniques is described in this paper. It is undertaken in several steps. A dense DSM is obtained by stereo image matching and then the results of multi-band classification, the DSM, and Normalized Difference Vegetation Index (NDVI) are used to reveal preliminary building interest areas. From these areas, a shape modeling algorithm has been used to precisely delineate their boundaries. The Dempster-Shafer data fusion technique is then applied to detect buildings from the combination of three data sources by a statistically-based classification. A number of test areas, which include buildings of different sizes, shape, and roof color have been investigated. The tests are encouraging and demonstrate that all processes in this system are important for effective building detection.

In situ observation of bainite growth during isothermal holding

The mechanism of bainite growth has been investigated using in situ transmission electron microscopy observations. It was found that, in a number of alloys studied, a bainitic embryo is made of basic transformation units. These units are either a group of stacking faults or, in two dimensions, a series of parallelograms of different sizes. Thickening/widening of the bainite embryo takes place through shear along the stacking fault planes or twining planes. The bainite embryo is elongated by the formation of new transformation units at both tips of the bainite plate. The three-dimensional morphology of bainite is a convex tens-like lath. It is believed that the bainite embryo grows by shearing, which is controlled by the diffusion of solute atoms during the transformation. As the growth rate is much lower than that of martensite, it is therefore detectable. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a metachain to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely. [Bayesian phylogenetic inference; heating parameter; Markov chain Monte Carlo; replicated chains.]

The pearl oysters, Pinctada maxima and P margaritifera, respond in different ways to culture in dissimilar environments

Growth, Condition Index (CI) and survival of the pearl oysters, Pinctada maxima and R margaritifera, were measured in three size groups of oysters over 14 months at two dissimilar environments in the Great Barrier Reef lagoon. These were the Australian Institute of Marine Science (AIMS) in a mainland bay and Orpheus Island Research Station (OIRS) in coral reef waters. Temperature, suspended particulate matter (SPM) and particulate organic matter (POM) were monitored during the study. Temperature at AIMS fluctuated more widely than at OIRS both daily and seasonally, with annual ranges 20-31 degrees C and 22-30 degrees C, respectively. Mean SPM concentration at AIMS (11.1 mg l(-1)) was much higher than at OIRS (1.4 mg l(-1)) and fluctuated widely (2-60 mg l(-1)). Mean POM level was also substantially higher at AIMS, being 2.1 mg l(-1) compared with 0.56 mg l(-1) at OIRS. Von Bertalatiffy growth curve analyses showed that P. maxima grew more rapidly and to larger sizes than P. margaritifera at both sites. For the shell height (SH) of R maxima, growth index phi'=4.31 and 4.24, asymptotic size SHinfinity = 229 and 205 mm, and time to reach 120 mm SH (T-(120))= 1.9 and 2.1 years at AIMS and OIRS, respectively. While for P margaritifera, phi'=4.00 and 4.15, SHinfinity = 136 and 157 mm, and T-(120) = 2.5 and 3.9 years at AIMS and OIRS, respectively. R maxima had significantly lower growth rates and lower survival of small oysters during winter compared with summer. There were, however, no significant differences between the two sites in growth rates of P. maxima and final Cl values. In contrast, P. margaritifiera showed significant differences between sites and not seasons, with lower growth rates, survival of small oysters, final Cl values and asymptotic sizes at AIMS. The winter low temperatures, but not high SPM at AIMS, adversely affected P. maxima. Conversely, the high SPM levels at AIMS, but not temperature, adversely affected P. margaritifera. This was in accordance with earlier laboratory-based energetics studies of the effects of temperature and SPM on these two species. P maxima has potential to be commercially cultured in ca. > 25 degrees C waters with a wide range of SPM levels, including oligotrophic coral reef waters with appropriate particle sizes. It is possible to culture R margaritifera in turbid conditions, but its poor performance in these conditions makes commercial culture unlikely. (c) 2005 Elsevier B.V. All rights reserved.